On optimal mechanism design for a sequencing problem

We study mechanism design for a single-server setting where jobs require compensation for waiting, while waiting cost is private information to the jobs. With given priors on the private information of jobs, we aim to find a Bayes–Nash incentive compatible mechanism that minimizes the total expected payments to the jobs. Following earlier work in the auction literature, we show that this problem is solved, in polynomial time, by a version of Smith’s rule. When both waiting cost and processing times are private, we show that optimal mechanisms generally do not satisfy an independence condition known as IIA, and conclude that a closed form for optimal mechanisms is generally not conceivable.

[1]  Danielle M. Varda,et al.  A Network Perspective , 2009 .

[2]  E. Maasland,et al.  Auction Theory , 2021, Springer Texts in Business and Economics.

[3]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[4]  Anna R. Karlin,et al.  On profit maximization in mechanism design , 2007 .

[5]  Rudolf Müller,et al.  Characterization of Revenue Equivalence , 2008 .

[6]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[7]  Herbert Hamers,et al.  On the balancedness of multiple machine sequencing games , 1999, Eur. J. Oper. Res..

[8]  Daniel R. Vincent,et al.  Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model , 2010 .

[9]  Manipushpak Mitra.  Mechanism design in queueing problems , 2001 .

[10]  Rakesh V. Vohra,et al.  Optimization and mechanism design , 2012, Mathematical Programming.

[11]  Rakesh V. Vohra,et al.  Optimal auctions with financially constrained buyers , 2008, J. Econ. Theory.

[12]  Fan Chung Graham,et al.  Internet and Network Economics, Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings , 2007, WINE.

[13]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[14]  M. Armstrong.  Optimal Multi-Object Auctions , 2000 .

[15]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[16]  Manipushpak Mitra,et al.  Simple sequencing problems with interdependent costs , 2004, Games Econ. Behav..

[17]  Rudolf Müller,et al.  Optimal Mechanisms for Single Machine Scheduling , 2008, WINE.

[18]  Alex Gershkov,et al.  On the equivalence of Bayesian and dominant strategy implementation for environments with nonlinear utilities , 2019 .

[19]  J. Suijs.  On incentive compatibility and budget balancedness in public decision making , 1996 .

[20]  Dilip Mookherjee,et al.  Dominant Strategy Implementation of Bayesian incentive Compatible Allocation Rules , 1992 .

[21]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[22]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[23]  Rudolf Müller,et al.  Weak monotonicity and Bayes-Nash incentive compatibility , 2007, Games Econ. Behav..

[24]  Ruben Hoeksma,et al.  Two Dimensional Optimal Mechanism Design for a Sequencing Problem , 2012, IPCO.

[25]  Hervé Moulin,et al.  On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs , 2007, Math. Oper. Res..

[26]  R. Vohra,et al.  An optimal auction for capacity constrained bidders: a network perspective , 2009 .

[27]  Chaitanya Swamy,et al.  Truthful mechanism design for multidimensional scheduling via cycle monotonicity , 2009, Games Econ. Behav..

[28]  Yang Cai,et al.  Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[29]  Carmine Ventre,et al.  Collusion-Resistant Mechanisms with Verification Yielding Optimal Solutions , 2008, TOCT.

[30]  Benny Moldovanu,et al.  Priority Auctions and Queue Disciplines That Depend on Processing Time , 2005, Manag. Sci..